Global Equivalence for Deformable Theormoeleastic Bodies

We consider equilibria arising in a model for phase transitions which correspond to stable critical points of the constrained variational problem Here W is a double‐well potential and is a strictly convex domain. For ε small, this is closely related to the problem of partitioning Ω into two subdomains of fixed volume, where the subdomain boundaries correspond to the transitional boundary between phases. Motivated by this geometry problem, we show that in a strictly convex domain, stable critical points of the original variational problem have a connected, thin transition layer separating the two phases. This relates to work in [GM] where special geometries such as cylindrical domains were treated, and is analogous to the results in [CHo] which show that in a convex domain, stable critical points of the corresponding unconstrained problem are constant. The proof of connectivity employs tools from geometric measure theory including the co‐area formula and the isoperimetric inequality on manifolds. The thinness of the transition layer follows from a separate calculation establishing spatial decay of solutions to the pure phases. (Accepted July 15, 1996)     

Characters of Fundamental Representations of Quantum Affine Algebras

We give closed formulae for the q-characters of the fundamental representations of the quantum loop algebra of a classical Lie algebra, in terms of a family of partitions satisfying some simple properties. We also give the multiplicities of the eigenvalues of the imaginary subalgebra in terms of these partitions.     

Magnetic and electrokinetic manipulations on a microchip device for bead-based immunosensing applications

The combination of electrophoretic and magnetic manipulations with electrochemical detection for a versatile microfluidic and bead-based biosensing application is demonstrated. Amperometric detection is performed in an off-channel setup by means of a voltammetric cell built at the microchannel outlet and using a gold working electrode. Superparamagnetic particles are introduced and handled inside the channel by means of an external permanent magnet in combination with the electrogenerated flow which allows reproducible loading. The specific detection of phenol as electroactive alkaline phosphatase product is used in this study as proof of concept for a sensitive protein quantification. Characterizations and optimization of different parameters have been carried out in order to achieve the best detection signal. The applicability of the device has been finally demonstrated by the detection of rabbit IgG as model protein after an immunoassay performed on magnetic particles as immobilization platform. A comparison between the electrochemical detection using the developed device and the optical standard detection revealed similar performances with, however, extremely lower amount of reagent used and shorter analysis time. The developed electrophoretic- and magnetic-based chip may open the way to several other biosensing applications with interest not only for other proteins but also for DNA analysis, cell counting, and environmental control.     

A macrocyclic ligand as receptor and Zn(II)-complex receptor for anions in water: binding properties and crystal structures

Binding properties of 24,29-dimethyl-6,7,15,16-tetraoxotetracyclo[19.5.5.0(5,8).0(14,17)]-1,4,9,13,18,21,24,29-octaazaenatriaconta-Δ(5,8),Δ(14,17)-diene ligand L towards Zn(II) and anions, such as the halide series and inorganic oxoanions (phosphate (Pi), sulfate, pyrophosphate (PPi), and others), were investigated in aqueous solution; in addition, the Zn(II)/L system was tested as a metal-ion-based receptor for the halide series. Ligand L is a cryptand receptor incorporating two squaramide functions in an over-structured chain that connects two opposite nitrogen atoms of the Me(2)[12]aneN(4) polyaza macrocyclic base. It binds Zn(II) to form mononuclear species in which the metal ion, coordinated by the Me(2)[12]aneN(4) moiety, lodges inside the three-dimensional cavity. Zn(II)-containing species are able to bind chloride and fluoride at the physiologically important pH value of 7.4; the anion is coordinated to the metal center but the squaramide units play the key role in stabilizing the anion through a hydrogen-bonding network; two crystal structures reported here clearly show this aspect. Free L is able to bind fluoride, chloride, bromide, sulfate, Pi, and PPi in aqueous solution. The halides are bound at acidic pH, whereas the oxoanions are bound in a wide range of pH values ranging from acidic to basic. The cryptand cavity, abundant in hydrogen-bonding sites at all pH values, allows excellent selectivity towards Pi to be achieved mainly at physiological pH 7.4. By joining amine and squaramide moieties and using this preorganized topology, it was possible, with preservation of the solubility of the receptor, to achieve a very wide pH range in which oxoanions can be bound. The good selectivity towards Pi allows its discrimination in a manner not easily obtainable with nonmetallic systems in aqueous environment.     

Wave Propagation along Axes of Symmetry in Linearly Elastic Media with Initial Stress

The proofs of the Fedorov–Stippes and Fedorov's theorems, which hold for linearly elastic homogeneous bodies in natural configurations, remain valid for any linearly elastic medium with initial stress provided that Hooke's tensor be replaced by a suitable elasticity tensor.     

Uniqueness theorems for the entropy in any differential body of complexity one

Uniqueness theorems for the entropy in any differential body of complexity one